Annette here from Shopify support. :)
The variant limit of 100 variants per product cannot be raised for any account or plan.
You can split one product up into several separate products and so increase the number of available variants.
For example, say your product is a box that comes in different materials (wood, metal, cardboard), sizes and colours. You could create 3 separate products: Wooden box, Metal box and Cardboard box with 100 size or colour variants each. Organising your products this way means you would be able to have 300 variants of a box on your store instead of 100.
I hope this workaround helps, if you would like to let us know what your products are, we could give more specific help.
I know you do not want to use any apps for this but just in case anyone else reading this would, the following apps will allow you to create products with more variants:
Adam, we encountered this problem as well (some of our products had >2k variants). We wound up engaging a third party to write an add-on that met our specific needs:
1. Support products split by style and color, which got us under the 100-variant limit
2. Ease navigation among different style/color combos using clickable color swatches
3. Don't make other stuff harder (e.g. by introducing weird data arrangements that you have to account for elsewhere).
What we have works, but is not without its problems. Chiefly, it does still affect our customers' browsing experience (same product in different colors can crowd out other products that were visible on our previous site). All of the workarounds that we have examined feel like a cure that's worse than the disease. It's low on our list of things to address, but it is there.
Company (if that is your real name), the limitation applies to all levels of Shopify service including Plus.
Does it make you curious? It sure makes me curious, since it seems arbitrary from the outside. That they have stuck to the limit all these years makes me think it is a deeply ingrained limitation, one that would be painful to remove.